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# Full text of "Analytical Mechanics"

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```WORK                      .                 16'
Therefore the work done against the gravitational force ii taking a body from one position to another depends only upoi the vertical height through which the body is raised and no upon the path.
130.   Dimensions and Units of Work.  Work is a scala magnitude and has for its dimensions [ML2T~2].   The C.G.8 unit of work is the erg.    It equals the work done by a fore of one dyne in displacing a particle through a distance o one centimeter, measured along its line of action.    It i
symbolized by -:~.   The erg is a small unit, therefor sec.2
a larger unit called the joule is also used. 1 joule = 107 ergs.
The British unit of work is the foot-pound (ft.4b.). It i the work done against the gravitational attraction of th earth in lifting one pound through a vertical distance o one foot. Since the work done in lifting bodies is mgh, w can express the foot-pound in terms of the fundamenta units, thus
1 ft. Ib. = 1 pd. X 32.2;^ X 1 ft. = 32.2
where pd. represents the pound-mass.
131.   Work Done by Components of Force.The work don by a force F in giving a particle a displacement ds is F cos 6 <& where 0 is the angle between F and ds.    Let X, Y, and Z b the rectangular components of F, then the direction of I
X   Y         7
is defined by its direction cosines -=,, and .   Therefor
b   b          F
if Z, m, and n denote the direction cosines of ds, we get
.    -.X .      Y .     Z* cos0=Z- + m~ +n~
* See Appendix Aiv.
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